Evaluating Improper Integrals Using Polar Coordinates

[iamwilson]

Homework Statement

A.Using polar coordinates, evaluate the improper integral of e^(-10(x^2+y^2))dxdy
B. use part A to integrate from negative infinity to positive infinity of e^(-10x^2)dx

2. Homework Equations [/b]

The Attempt at a Solution

i got part A to be pi/10, but for part B i clueless, can someone please give me a hit on how to integrate it!

 

[Dick]

pi/10 looks ok. But for the second part you aren't supposed to do another integration. You are supposed to realize the first integral can be split into the product of a dx integral and a dy integral both of which look the same. Use exp(-10(x^2+y^2))=exp(-10x^2)*exp(-10y^2).